A kinetic neutral atom model for tokamak scrapeoff layer tubulence simulations. Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva


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1 A kinetic neutral atom model for tokamak scrapeoff layer tubulence simulations Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva CRPP  EPFL SPS Annual Meeting CRPP
2 The tokamak scrapeoff layer (SOL) Open field lines Heat exhaust Confinement Impurities Fusion ashes removal Fueling the plasma (recycling) Three regimes Convection limited Conduction limited Detached Christoph Wersal  CRPP Neutral particles and SOL turbulence 2 / 14
3 Convection limited regime Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
4 Convection limited regime Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
5 Convection limited regime Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
6 Convection limited regime Low plasma density Long λ mfp for neutrals Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
7 Convection limited regime Low plasma density Long λ mfp for neutrals Ionization in the core Ionization Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
8 Convection limited regime Low plasma density Long λ mfp for neutrals Ionization in the core Heat particle source Ionization Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
9 Convection limited regime Low plasma density Long λ mfp for neutrals Ionization in the core Heat particle source Ionization Q is mainly convective Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 3 / 14
10 Conduction limited regime High plasma density Christoph Wersal  CRPP Neutral particles and SOL turbulence 4 / 14
11 Conduction limited regime High plasma density Short λ mfp Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 4 / 14
12 Conduction limited regime High plasma density Short λ mfp Ionization close to targets Ionization Neutrals Christoph Wersal  CRPP Neutral particles and SOL turbulence 4 / 14
13 Conduction limited regime High plasma density Short λ mfp Ionization close to targets Temperature gradients form Q is mainly conductive Neutrals Ionization Christoph Wersal  CRPP Neutral particles and SOL turbulence 4 / 14
14 The GBS code, a tool to simulate SOL turbulence Driftreduced Braginskii equations d/dt ω ci,k 2 k 2 Evolves scalar fields in 3D geometry n,ω,v e,v,i,t e,t i Fluxdriven, no separation between equilibrium and fluctuations Power balance between plasma outflow from the core, turbulent transport, and sheath losses [Ricci et al., PPCF, 2012] No divertor geometry No neutral physics Christoph Wersal  CRPP Neutral particles and SOL turbulence 5 / 14
15 The model Introduction The neutrals model Conclusions Kinetic model for the neutral atoms with Krook operators f n t + v f n x = ν ionf n ν cx (f n n n Φ i ) + ν rec n i Φ i (1) ν ion = n e v e σ ion (v e ), ν cx = n i v rel σ cx (v rel ) ν rec = n e v e σ rec (v e ), Boundary conditions Φ i = f i /n i (v in respect to the surface; θ between v and normal vector to the surface) dv v f n ( x w, v) + u i n i = 0 (2) f n ( x w, v) cos(θ)e mv 2 /2T w for v > 0 Christoph Wersal  CRPP Neutral particles and SOL turbulence 6 / 14
16 The model Introduction The neutrals model Conclusions Kinetic model for the neutral atoms with Krook operators f n t + v f n x = ν ionf n ν cx (f n n n Φ i ) + ν rec n i Φ i (1) ν ion = n e v e σ ion (v e ), ν cx = n i v rel σ cx (v rel ) ν rec = n e v e σ rec (v e ), Boundary conditions Φ i = f i /n i (v in respect to the surface; θ between v and normal vector to the surface) dv v f n ( x w, v) + u i n i = 0 (2) f n ( x w, v) cos(θ)e mv 2 /2T w for v > 0 Christoph Wersal  CRPP Neutral particles and SOL turbulence 6 / 14
17 The model Introduction The neutrals model Conclusions Kinetic model for the neutral atoms with Krook operators f n t + v f n x = ν ionf n ν cx (f n n n Φ i ) + ν rec n i Φ i (1) ν ion = n e v e σ ion (v e ), ν cx = n i v rel σ cx (v rel ) ν rec = n e v e σ rec (v e ), Boundary conditions Φ i = f i /n i (v in respect to the surface; θ between v and normal vector to the surface) dv v f n ( x w, v) + u i n i = 0 (2) f n ( x w, v) cos(θ)e mv 2 /2T w for v > 0 Christoph Wersal  CRPP Neutral particles and SOL turbulence 6 / 14
18 The model Introduction The neutrals model Conclusions Kinetic model for the neutral atoms with Krook operators f n t + v f n x = ν ionf n ν cx (f n n n Φ i ) + ν rec n i Φ i (1) ν ion = n e v e σ ion (v e ), ν cx = n i v rel σ cx (v rel ) ν rec = n e v e σ rec (v e ), Boundary conditions Φ i = f i /n i (v in respect to the surface; θ between v and normal vector to the surface) dv v f n ( x w, v) + u i n i = 0 (2) f n ( x w, v) cos(θ)e mv 2 /2T w for v > 0 Christoph Wersal  CRPP Neutral particles and SOL turbulence 6 / 14
19 The model Introduction The neutrals model Conclusions Kinetic model for the neutral atoms with Krook operators f n t + v f n x = ν ionf n ν cx (f n n n Φ i ) + ν rec n i Φ i (1) ν ion = n e v e σ ion (v e ), ν cx = n i v rel σ cx (v rel ) ν rec = n e v e σ rec (v e ), Boundary conditions Φ i = f i /n i (v in respect to the surface; θ between v and normal vector to the surface) dv v f n ( x w, v) + u i n i = 0 (2) f n ( x w, v) cos(θ)e mv 2 /2T w for v > 0 Christoph Wersal  CRPP Neutral particles and SOL turbulence 6 / 14
20 The model in steady state Steady state, f n t = 0, first approach Valid if τ neutral losses < τ turbulence e.g. T e = 20eV, n 0 = m 3 τ loss ν 1 eff s τ turbulence R 0 L p /c s s Otherwise: time dependent model Christoph Wersal  CRPP Neutral particles and SOL turbulence 7 / 14
21 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 v 0 x Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
22 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 v 0 x f n (x,v) (3) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
23 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 v 0 x f n (x,v) = x 0 dx (3) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
24 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 0 x' x v f n (x,v) = x 0 dx ν cx (x )n n (x )Φ i (x,v) v (3) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
25 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 0 x' x v f n (x,v) = x 0 dx ν cx (x )n n (x )Φ i (x,v) e 1 x v x dx (ν cx (x )+ν ion (x )) v (3) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
26 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 0 x' x v f n (x,v) = x 0 dx ν cx (x )n n (x )Φ i (x,v) e 1 x v x dx (ν cx (x )+ν ion (x )) v (3) + f w (v)e 1 v x0 dx (ν cx (x )+ν ion (x )) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
27 The method of characteristics Example in 1D, no recombination, v > 0 and a wall at x = 0 0 x' x v f n (x,v) = x 0 dx ν cx (x )n n (x )Φ i (x,v) e 1 x v x dx (ν cx (x )+ν ion (x )) v (3) + f w (v)e 1 v x0 dx (ν cx (x )+ν ion (x )) Christoph Wersal  CRPP Neutral particles and SOL turbulence 8 / 14
28 An equation for the density distribution By imposing dv f n = n n n n (x) = x dx n n (x ) contribution by v < 0 + n w (x) dv ν cx(x )Φ i (x,v) v e ν eff (x x ) v (4) we get an integral equation for n n (x). Christoph Wersal  CRPP Neutral particles and SOL turbulence 9 / 14
29 Discretized equations Discretize the spatial direction in x x i and n n (x i ) n i n nn i = nn j j i 0 dv ν cx(x j )Φ i (x j,v) e ν eff (x i x j ) v (5) v + contribution by v < 0 + n w (x i ) System of linear equations, solved with standard methods Christoph Wersal  CRPP Neutral particles and SOL turbulence 10 / 14
30 Selfconsistent simulation with GBS and neutrals model Plasma: snapshot of density, parallel ion velocity and electron temperature from GBS Christoph Wersal  CRPP Neutral particles and SOL turbulence 11 / 14
31 Selfconsistent simulation with GBS and neutrals model Neutral density distribution and ionization rate (n n n e v e σ ion ) from the simple neutral model, n 0 = m 3, T 0 = 10eV Christoph Wersal  CRPP Neutral particles and SOL turbulence 12 / 14
32 Conclusions Developement of a neutral model for GBS Kinetic equation with Krook operators for ion, rec and cx 2D evaluation of the neutral density shows its proximity to the limiter Christoph Wersal  CRPP Neutral particles and SOL turbulence 13 / 14
33 Outlook Find the transition from convection to conduction limited regime Relax the steady state assumption Adding density source, drag force, and temperature source/sink to the equations in GBS Move towards detachment Divertor geometry Radiative detachment in limited geometry Mimic the geometry of one divertor leg Christoph Wersal  CRPP Neutral particles and SOL turbulence 14 / 14
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